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Natural divisors and the brownian motion

Eugenijus Manstavičius — 1996

Journal de théorie des nombres de Bordeaux

A model of the Brownian motion defined in terms of the natural divisors is proposed and weak convergence of the related measures in the space 𝐃 [0,1] is proved. An analogon of the Erdös arcsine law, known for the prime divisors [6] (see [14] for the proof), is obtained. These results together with the author’s investigation [15] extend the systematic study [9] of the distribution of natural divisors. Our approach is based upon the functional limit theorems of probability theory.

Discrete limit laws for additive functions on the symmetric group

Eugenijus Manstavičius — 2005

Acta Mathematica Universitatis Ostraviensis

Inspired by probabilistic number theory, we establish necessary and sufficient conditions under which the numbers of cycles with lengths in arbitrary sets posses an asymptotic limit law. The approach can be extended to deal with the counts of components with the size constraints for other random combinatorial structures.

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